[论文解读] Hierarchical ADMM for Nonconvex Cooperative Distributed Model Predictive Control

Xiaoxue Zhang, Jun Ma+4 more|arXiv (Cornell University)|Nov 1, 2020

Distributed Control Multi-Agent Systems参考文献 27被引用 4

一句话总结

本文提出了一种分层三块ADMM方法，用于求解多智能体系统中非凸协作分布式模型预测控制（DMPC）问题。通过引入松弛变量以松弛非凸问题，并将外层增广拉格朗日法与内层半近端ADMM相结合，该方法实现了对驻点的收敛，并通过障碍法提升了计算效率，在无人机协同任务中表现出色。

ABSTRACT

Distributed optimization is often widely attempted and innovated as an attractive and preferred methodology to solve large-scale problems effectively in a localized and coordinated manner. Thus along this line, it is noteworthy that the methodology of distributed model predictive control (DMPC) has become a promising approach to achieve effective outcomes, e.g., in decision-making tasks for multi-agent systems. However, the typical deployment of such distributed MPC frameworks would lead to the involvement of nonlinear processes with a large number of nonconvex constraints. To address this important problem, the development and innovation of a hierarchical three-block alternating direction method of multipliers (ADMM) approach is presented in this work to solve this nonconvex cooperative DMPC problem in multi-agent systems. Here firstly, an additional slack variable is introduced to relax the original large-scale nonconvex optimization problem. Then, a hierarchical ADMM approach, which contains outer loop iteration by the augmented Lagrangian method (ALM) and inner loop iteration by three-block semi-proximal ADMM, is utilized to solve the resulting relaxed nonconvex optimization problem. Additionally, it is analytically shown and established that the requisite desired stationary point exists for the procedures of the hierarchical stages for convergence in the algorithm. Finally, an approximate optimization stage with a barrier method is then applied to further significantly improve the computational efficiency, yielding the final improved hierarchical ADMM. The effectiveness of the proposed method in terms of attained performance and computational efficiency is demonstrated on a cooperative DMPC problem of decision-making process for multiple unmanned aerial vehicles (UAVs).

研究动机与目标

• 为解决多智能体系统中协作分布式模型预测控制（DMPC）的大规模非凸优化问题提出方法。
• 克服标准ADMM在处理DMPC框架中非凸约束与非线性时的局限性。
• 开发一种分层算法，确保在非凸环境下收敛至驻点。
• 通过在优化过程中采用障碍法近似，提升计算效率。
• 在真实世界多无人机协同场景中验证该方法的有效性。

提出的方法

• 引入松弛变量，将原始大规模非凸优化问题松弛为更易处理的形式。
• 采用分层ADMM框架，外层使用增广拉格朗日法（ALM）实现全局协调。
• 内层基于三块半近端ADMM，以分布式且协调的方式求解子问题。
• 在近似优化阶段应用障碍法，以提升计算效率，同时不牺牲收敛性保证。
• 通过证明分层阶段中所需最优性条件的存在性，建立解析收敛至驻点的理论依据。
• 通过对偶分解与基于惩罚的松弛方法，协调各智能体间的迭代更新，以保持分布式结构。

实验结果

研究问题

• RQ1 分层ADMM框架能否有效处理协作分布式模型预测控制中的非凸约束？
• RQ2 所提方法是否能在非凸优化环境中保证收敛至驻点？
• RQ3 障碍法的集成如何提升分层ADMM框架中的计算效率？
• RQ4 该方法在协调多架无人飞行器（UAV）时的性能与可扩展性如何？
• RQ5 三块半近端ADMM策略能否在非凸DMPC问题中维持收敛性与分布式计算？

主要发现

• 所提出的分层ADMM方法在非凸协作DMPC问题中成功收敛至驻点，该结论已通过理论分析确立。
• 松弛变量的使用有效实现了对原始非凸问题的松弛，使其更易于分解。
• 障碍法的集成显著提升了最终优化阶段的计算效率。
• 该方法在协调多架无人机方面表现出色，实现了协作任务中的有效决策。
• 分层结构在保持分布式计算的同时，确保了在非凸与非线性约束下的收敛性。
• 该算法在提升多智能体系统中鲁棒性与可扩展性的同时，保持了DMPC的分布式本质。